Charge is distributed throughout a spherical shell of inner radius T₁ and outer radius ₂ with a volume density given by p= Pori/r, where Po is a constant. Following the next few steps outlined, determine the electric field due to this charge as a function of r, the distance from the center of the shell. Hint a. Let's start from outside-in. For a spherical Gaussian surface of radius > ₂, how much charge is enclosed inside this Gaussian surface? Hint for finding total charge Qend (Answer in terms of given quantities, Po. 7₁, 7₂, and physical constants and/or £g. Use underscore ("") for subscripts, and spell out Greek letters.) b. What is the electric field as a function of for distances greater than 72? Finish the application of Gauss's Law to find the electric field as a function of distance. E(r>r₂): c. Now let's work on the "mantle" layer, ₁ << 7₂. For a spherical surface of radius between T₁ and 7₂. how much charge is enclosed inside this Gaussian surface? Hint for finding charge within Qendl (r) (Answer in terms of given quantities and the variable r.) d. What is the electric field as a function of for distances between 1 and ₂? Finish the application of Gauss's Law to find the elcetric field as a function of distance. E(r) for T₁
Charge is distributed throughout a spherical shell of inner radius T₁ and outer radius ₂ with a volume density given by p= Pori/r, where Po is a constant. Following the next few steps outlined, determine the electric field due to this charge as a function of r, the distance from the center of the shell. Hint a. Let's start from outside-in. For a spherical Gaussian surface of radius > ₂, how much charge is enclosed inside this Gaussian surface? Hint for finding total charge Qend (Answer in terms of given quantities, Po. 7₁, 7₂, and physical constants and/or £g. Use underscore ("") for subscripts, and spell out Greek letters.) b. What is the electric field as a function of for distances greater than 72? Finish the application of Gauss's Law to find the electric field as a function of distance. E(r>r₂): c. Now let's work on the "mantle" layer, ₁ << 7₂. For a spherical surface of radius between T₁ and 7₂. how much charge is enclosed inside this Gaussian surface? Hint for finding charge within Qendl (r) (Answer in terms of given quantities and the variable r.) d. What is the electric field as a function of for distances between 1 and ₂? Finish the application of Gauss's Law to find the elcetric field as a function of distance. E(r) for T₁
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Transcribed Image Text:Charge is distributed throughout a spherical shell of inner radius and outer radius 72 with a
volume density given by p= Pori/r, where Po is a constant. Following the next few steps outlined,
determine the electric field due to this charge as a function of 7, the distance from the center of the
shell.
Hint
a. Let's start from outside-in. For a spherical Gaussian surface of radius > ₂ how much
charge is enclosed inside this Gaussian surface?
Hint for finding total charge
Qencl
(Answer in terms of given quantities, Po. 71, 72, and physical constantske and/or £g. Use
underscore ("_") for subscripts, and spell out Greek letters.)
b. What is the electric field as a function of for distances greater than 72? Finish the application
of Gauss's Law to find the electric field as a function of distance.
E(T > T₂)
c. Now let's work on the "mantle" layer, ₁ <<₂. For a spherical surface of radius & between
T₁ and ₂. how much charge is enclosed inside this Gaussian surface?
Hint for finding charge within
Qendl (7)
(Answer in terms of given quantities and the variable r.)
d. What is the electric field as a function of r for distances between ₁ and 2? Finish the
application of Gauss's Law to find the elcetric field as a function of distance.
for r₁ < F< T₂.
E(r)
e. What is the electric field for distances less than ₁?
E(r<ri)
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Step 1: Determine the given data:
VIEWStep 2: a) Find the total charge enclosed for r>r2:
VIEWStep 3: b) Find the electric field at r>r2:
VIEWStep 4: c) Calculate the charge enclosed within the Gaussian surface for r1<r<r2:
VIEWStep 5: d) Find the electric field at r1<r<r2:
VIEWStep 6: e. Find the electric field at r<r1:
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